Properties

Label 446400.mp
Number of curves 22
Conductor 446400446400
CM no
Rank 00
Graph

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Copy content sage:E = EllipticCurve("mp1") E.isogeny_class()
 

Elliptic curves in class 446400.mp

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446400.mp1 446400mp1 [0,0,0,1140300,550342000][0, 0, 0, -1140300, 550342000] 1482713947827/325058560-1482713947827/325058560 35948876267520000000-35948876267520000000 [][] 92897289289728 2.47312.4731 Γ0(N)\Gamma_0(N)-optimal
446400.mp2 446400mp2 [0,0,0,8075700,3306042000][0, 0, 0, 8075700, -3306042000] 722458663317/476656000722458663317/476656000 38428754116608000000000-38428754116608000000000 [][] 2786918427869184 3.02243.0224  

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 446400.mp have rank 00.

Complex multiplication

The elliptic curves in class 446400.mp do not have complex multiplication.

Modular form 446400.2.a.mp

Copy content sage:E.q_eigenform(10)
 
q+q73q114q13+6q17+q19+O(q20)q + q^{7} - 3 q^{11} - 4 q^{13} + 6 q^{17} + q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.